The major purpose of this study was to investigate factors and challenges that hindered effective teaching of mathematics for understanding in senior secondary schools in the Omusati Education Region in Namibia. The study investigated how the participants dealt with identified challenges in the mathematics classrooms in selected senior secondary schools. Further, the study attempted to establish necessary support and / or training opportunities that mathematics teachers might need to ensure effective application of teaching mathematics for understanding in their regular classrooms. The sample was made up of eight senior secondary schools out of the population of 12 senior secondary schools in the Omusati Education Region. The schools were selected from the school circuits using maximum variation and random sampling techniques. Twenty out of 32 mathematics teachers from eight selected senior secondary schools in the Omusati Education Region responded to the interviews and two lessons per participant were observed. Interviews and observations were used to collect data from the 20 senior secondary school mathematics teachers with respect to teaching mathematics for understanding. Frequency tables, pie charts and bar graphs were used to analyze the data collected. The results indicated that teaching for understanding was little observed in mathematics classrooms. Part of the challenges identified were, overcrowded classrooms, lack of teaching and learning resources, lack of support from advisory teachers, and automatic promotions, among others. Mathematics teachers needed induction programmes, in-service training opportunities, and advisory services amongst others in order to be able to teach mathematics effectively. The study recommended that teaching for understanding should be researched in all subjects in Namibian classrooms and should be made clearly understood by all teachers in order to be able to use and apply it during their teaching. New teachers should be provided with induction programmes to give them support and tools at the beginning of their teaching careers. Further research on teaching for understanding should be conducted in other school subjects in Namibia in order to ensure teaching for understanding across the curriculum.

Key words: teaching, understanding.

Sensory substitution constitutes an interesting domain of study to consider the philosopher’s classical question of distal attribution: how we can distinguish between a sensation and the perception of an object that causes this sensation. We tested the hypothesis that distal attribution consists of three distinct components: an object, a perceptual space, and a coupling between subjects’ movements and stimulation. We equipped sixty participants with a visual-to-auditory substitution device, without any information about it. The device converts the video stream produced by a head-mounted camera into a sound stream. We investigated several experimental conditions: the existence or not of a correlation between movements and resulting stimulation, the direct or indirect manipulation of an object, and the presence of a background environment. Participants were asked to describe their impressions by rating their experiences in terms of seven possible “scenarios”. These scenarios were carefully chosen to distinguish the degree to which the participants attributed their sensations to a distal cause. Participants rated the scenarios both before and after they were given the possibility to interrupt the stimulation with an obstacle. We were interested in several questions. Did participants extract laws of co-variation between their movements and resulting stimulation? Did they deduce the existence of a perceptual space originating from this coupling? Did they individuate objects that caused the sensations? Whatever the experimental conditions, participants were able to establish that there was a link between their movements and the resulting auditory stimulation. Detection of the existence of a coupling was more frequent than the inferences of distal space and object.

Key words: sensory substitution, distal attribution, space, object, objecthood, sensorimotor theory, sensorimotor coupling.

The question of closure in biological systems is central to understanding the origins of the biological variation and complexity upon which various forms of selection act. Much of evolutionary theory, especially in the second half of the twentieth century, is concerned with the consequences of environmental selection acting on biodiversity, but neglects questions of the origin of that diversity. This has permitted us to act as if an explanation ofconsequences was the ultimate explanation in biology. However, Darwin understood that evolution was both information driven and information constrained. The link between evolutionary constraints and closure can be profitably explored by starting with Darwin’s notion of the primacy of “the nature of the organism” over “the nature of the conditions” articulated in the sixth edition of Origin of Species. Contemporary ideas of self-organization, emergence, complexity, and inherent (developmental and phylogenetic) constraints can be seen as an elaboration and refinement of Darwin’s views if we adopt the following perspective: (1) information is cheap, not costly, to produce, but may have costly consequences; and (2) information is produced by systems that are informationally closed but remain thermodynamically open.

In some domains acquiring knowledge has proved successful in ways that have not been equalled elsewhere notwithstanding long-term efforts. As the lack of success in the latter must be due to the combination of approach and content, this suggests searching for new approaches, and interpreting the ‘not’ as a possibly ‘never’. The alternative is to see the ‘not’ as a ‘not yet’. The argument Von Foerster (1970) brings to this dilemma is that in the social domain the ‘not’ is due to an extra, mainly action-bound, source of variation. Constraining this source will allow for a (reasonable) ‘not yet’. To remind of Heinz’s surprising and sophisticated argument it is re-used.

Traditional views in philosophy of mind and cognitive science depict the mind as an information processor, one whose connections with the body and the world are of little theoretical importance. On the contrary, mounting empirical evidence shows that bodily states and modality-specific systems for perception and action underlie information processing, and that embodiment contributes to various aspects and effects of mental phenomena. This article will briefly review and discuss some of this evidence and what it implies. By challenging mainstream accounts of mind and cognition, embodiment views offer new ways of conceptualizing knowledge and suggest novel perspectives on cognitive variation and mind-body reductionism. WIREs Cogn Sci 2013, 4:319–325. doi: 10. 1002/wcs. 1226

The invention of the computer has revolutionized science. With respect to finding the essential structures of life, for example, it has enabled scientists not only to investigate empirical examples, but also to create and study novel hypothetical variations by means of simulation: ‘life as it could be’. We argue that this kind of research in the field of artificial life, namely the specification, implementation and evaluation of artificial systems, is akin to Husserl’s method of free imaginative variation as applied to the specific regional ontology of biology. Thus, at a time when the clarification of the essence of our biological embodiment is of growing interest for phenomenology, we suggest that artificial life should be seen as a method of externalizing some of the insurmountable complexity of imaginatively varying the phenomenon of life.

The economic crisis has brought ethical issues into the foreground of public debate inviting a consideration of ethical wealth distribution. Issues in meta-ethics play a significant role in these discussions because they have such potential to vary from person to person, while remaining hidden. They include whether ethical ideas may be objectively correct or vary depending on context, whether ethical ideas are principally matters of reason or of emotion, whether men and women consider ethical questions from different viewpoints and finally here – ideas about the origins of altruism. These varied perspectives each contain widely varying ethical approaches. This paper began in the context of a course about ethics and inclusive education, however understanding the interplay of these ideas has broader significance because most people naturally wish to do good. Indeed, all disagreements about what people hold fundamentally important have the potential to lead to conflict and violence. Therefore, I believe a fuller appreciation of meta-ethical ideas and their variation has general implications for peaceful co-existence. Relevance: Constructivist theory has ethical implications that may be useful to understand conflict.

Key words: Ethics, meta-ethics, radical constructivism

The aim of the present chapter is to examine attitudes and images relating to inclusive education programmes with a view to understanding more fully the socio-emotional context within which inclusion takes place. This paper views conceptions of others, as social conservations in the Piagetian sense or as social constructions in a constructivist framework. A number of elements are brought to bear on this issue. They include examination of variations in children’s representations of intellectual disability and Down Syndrome, attitudes towards inclusive education and the issue of the validity of this type of attitude measure. Children in middle childhood are building their self-representations (Harter 1998), and we believe that representations of self and other develop together as youngsters mature. Further, there is good evidence that difficulties with peers place children at risk for developing psychological problems (Harter 1998). In a series of classroom intervention studies the first author has investigated children’s representations of their peers with special needs. Gender and grade level differences have consistently been found in these studies (Gash 1993; Gash and Coffey 1995; Gash 1996). Girls have been found to be more sociable, more socially concerned and more positive towards children with an intellectual disability than boys (Gash 1993). Older children have been found to be more socially concerned, more sociable and more positive towards integration (Gash 1993). Further, girls in a school with a special class were more socially concerned and sociable than peers in a similar school without this facility (Gash and Coffey 1995). Two sets of linked studies are described in this chapter. The first set is based on the use of questionnaire techniques to examine children’s attitudes towards intellectual disability and Down Syndrome. There are four studies in the first set. The first compares attitudes of samples of Irish and Spanish primary school pupils towards integrated or included pupils with intellectual disability. The second re-examines these cross-cultural findings through use of data requiring a more focused or restricted representation of intellectual disability, specifying Down Syndrome. The third provides evidence for the contextual validity of this attitude measure, and the fourth is an evaluation of a programme of integration at second level. The second set of studies examines in more detail children’s and parents’ attitudes towards integration and Down Syndrome. The first of these is a qualitative assessment of Irish and Spanish primary school pupils’ thinking about aspects of Down Syndrome, in particular inclusion of Down Syndrome children in their classrooms, and how pupils feel about socialising with peers with Down Syndrome. The second is based on a nationwide sample of 501 Irish farmers to assess their attitudes towards integration and its management in the Irish educational system. This provides data on adults’ attitudes towards integration. It is important to note that these data were collected just prior to 1996 and so reflect the Irish primary system at that time. Subsequently there has been a dramatic increase in the educational services for children in difficulty in many Irish schools. In the broader cultural domain the process of social identification is known to be important in the integration of minority groups into society (e.g. Lalonde et al. 1992). Learning to make friends and to have an identity in a group of friends is one of the tasks of childhood. A key element in the glue cementing a social group together is an individual’s acceptance of the attitudes that this particular group considers important. If a child is different from other children this matching of attitudes may be more difficult. In the microcosm of classroom or school, attitudes play a central role in determining the success of integration and inclusion. Negative attitudes on the part of teachers or students towards a child with a disability may arise because of limited experience (e.g. Hegarty 1993). Whatever their origin, negative attitudes are likely to affect the quality of classroom and school life. Helen Keller is known to have said that the heaviest burdens of disability arise from difficulties in social relations and not from the disability itself. The present studies are concerned principally with two types of attitudes in children. The first is about sociable acceptance and concern, and the second is about acceptance of integration and inclusion. While these two are not identical, they are closely linked to the context in which friendships are formed in school. In turn, friendships support good outcomes across development in childhood (e.g. Hartup 1983; 1996). Relevance: This paper relies on the idea that children’s ideas about others who are different are constructed on the basis of their experiences. Here differences between children in Ireland and Spain are examined for children of different ages in primary school with a view to relating these differences to the varying social contexts of the samples who participated in the studies. The view taken is that the ideas expressed are social versions of Piaget’s conservations. The hope is that the variation demonstrated provides teachers with opportunities to think about ways to stimulate discussion and promote tolerance which may potentially be dampened by stereotypes.

Key words: Stereotypes, children, social constructions, inclusive education, representation of disability

The terms “autonomy” and “self-direction” are being used more and more frequently in educational discussion. This article identifies and examines the ideas and historical contingencies which form the background to these developments, including minority rights movements, shifts in educational philosophy, reactions against behaviourism, linguistic pragmatism, wider access to education, increased internationalism, the commercialization of language provision and easier availability of educational technology. A number of objections to “autonomy” (it could not work with children or adults of low educational attainment, nor for “difficult” languages, or in examination-led syllabuses) have largely been overcome. Research into a wide range of educational topics, such as learning styles and strategies, resource centres and counsellor and learner training has directly contributed to present practice. Much remains to be done, however, particularly if cultural variation in learning attitudes, roles and activities is to be taken into account and if “autonomy” and “self-direction” are to be situated and understood within the workings of the social knowledge system.

In this article, we integrate two constructionist approaches – the theory of constructed emotion and rational constructivism – to introduce several novel hypotheses for understanding emotional development. We first discuss the hypothesis that emotion categories are abstract and conceptual, whose instances share a goal-based function in a particular context but are highly variable in their affective, physical, and perceptual features. Next, we discuss the possibility that emotional development is the process of developing emotion concepts, and that emotion words may be a critical part of this process. We hypothesize that infants and children learn emotion categories the way they learn other abstract conceptual categories – by observing others use the same emotion word to label highly variable events. Finally, we hypothesize that emotional development can be understood as a concept construction problem: a child becomes capable of experiencing and perceiving emotion only when her brain develops the capacity to assemble ad hoc, situated emotion concepts for the purposes of guiding behavior and giving meaning to sensory inputs. Specifically, we offer a predictive processing account of emotional development.

Key words: prediction, construction, variation, social learning, culture